Question

Find a quadratic polynomial whose sum and product of zeros are
$- \sqrt{2}$
and
$\frac{1}{3}$




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Answer 1

Step-by-step explanation:

$let \: \alpha \: and \: \beta \: be \: zeros \\ \\ atq = > \\ \alpha + \beta = - \sqrt{2} \\ \alpha \beta = \frac{1}{3} \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ {x}^{2} - ( - \sqrt{2} )x + \frac{1}{3} = 0 \\ 3 {x}^{2} + 3 \sqrt{2} x + 1 = 0$